Introductory Physics PHYS101

Transcription

1 Introductory Physics PHYS101

2 Dr Richard H. Cyburt Assistant Professor of Physics My office: 402c in the Science Building My phone: (304) My In person or is the best way to get a hold of me. PHYS101

3 My Office Hours TRF 9:30-11:00am F 12:30-2:00pm Meetings may also be arranged at other times, by appointment PHYS101

4 PHYS101: Introductory Physics 400 Lecture: 8:00-9:15am, TR Science Building Lab 1: 3:00-4:50pm, F Science Building 304 Lab 2: 1:30-3:20pm, M Science Building 304 Lab 3: 3:30-5:20pm, M Science Building 304 Lab 20: 6:00-7:50pm, M Science Building 304 PHYS101

5 Mastering Physics Online Go to HYPERLINK " Under Register Now, select Student. Confirm you have the information needed, then select OK! Register now. Enter your instructor s Course ID (RCYBURTPHYS101), and choose Continue. Enter your existing Pearson account username and password and select Sign in. You have an account if you have ever used a Pearson MyLab & Mastering product, such as MyMathLab, MyITLab, MySpanishLab, or MasteringChemistry. If you don t have an account, select Create and complete the required fields. Select an access option. Enter the access code that came with your textbook or was purchased separately from the bookstore. PHYS101

6 Introductory Physics PHYS101

7 Douglas Adams Hitchhiker s Guide to the Galaxy PHYS101

8 You re already know physics! You just don t necessarily know the terminology and language we use!!! Physics of NASCAR Physics of Anger Birds PHYS101

9 In class!! PHYS101

10 This lecture will help you understand: Acceleration Motion with constant Acceleration 1D problems in Motion Using Vectors Coordinate Systems and Vector Components PHYS101

11 Section 2.4 Acceleration

12 Acceleration We define a new motion concept to describe an object whose velocity is changing. The ratio of Δv x /Δt is the rate of change of velocity. The ratio of Δv x /Δt is the slope of a velocity-versus-time graph.

13 Units of Acceleration In our SI unit of velocity, 60 mph = 27 m/s. The Corvette speeds up to 27 m/s in Δt = 3.6 s. It is customary to abbreviate the acceleration units (m/s)/s as m/s 2, which we say as meters per second squared. Every second, the Corvette s velocity changes by 7.5 m/s.

14 Example 2.6 Animal acceleration Lions, like most predators, are capable of very rapid starts. From rest, a lion can sustain an acceleration of 9.5 m/s 2 for up to one second. How much time does it take a lion to go from rest to a typical recreational runner s top speed of 10 mph? PREPARE We can start by converting to SI units. The speed the lion must reach is The lion can accelerate at 9.5 m/s 2, changing its speed by 9.5 m/s per second, for only 1.0 s long enough to reach 9.5 m/s. It will take the lion less than 1.0 s to reach 4.5 m/s, so we can use a x = 9.5 m/s 2 in our solution.

15 Example 2.6 Animal acceleration (cont.) SOLVE We know the acceleration and the desired change in velocity, so we can rearrange Equation 2.8 to find the time: ASSESS The lion changes its speed by 9.5 meters per second in one second. So it s reasonable (if a bit intimidating) that it will reach 4.5 m/s in just under half a second.

16 Representing Acceleration An object s acceleration is the slope of its velocity-versus-time graph.

17 Representing Acceleration We can find an acceleration graph from a velocity graph.

18 QuickCheck 2.14 The motion diagram shows a particle that is slowing down. The sign of the position x and the sign of the velocity v x are: Position is positive, velocity is positive. Position is positive, velocity is negative. Position is negative, velocity is positive. Position is negative, velocity is negative.

19 QuickCheck 2.14 The motion diagram shows a particle that is slowing down. The sign of the position x and the sign of the velocity v x are: Position is positive, velocity is positive. Position is positive, velocity is negative. Position is negative, velocity is positive. Position is negative, velocity is negative.

20 Example Problem A ball moving to the right traverses the ramp shown below. Sketch a graph of the velocity versus time, and, directly below it, using the same scale for the time axis, sketch a graph of the acceleration versus time.

21 The Sign of the Acceleration An object can move right or left (or up or down) while either speeding up or slowing down. Whether or not an object that is slowing down has a negative acceleration depends on the direction of motion.

22 The Sign of the Acceleration (cont.) An object can move right or left (or up or down) while either speeding up or slowing down. Whether or not an object that is slowing down has a negative acceleration depends on the direction of motion.

23 QuickCheck 2.15 The motion diagram shows a particle that is slowing down. The sign of the acceleration a x is: Acceleration is positive. Acceleration is negative.

24 QuickCheck 2.15 The motion diagram shows a particle that is slowing down. The sign of the acceleration a x is: Acceleration is positive. Acceleration is negative.

25 QuickCheck 2.16 A cyclist riding at 20 mph sees a stop sign and actually comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph. Which is his motion diagram?

26 QuickCheck 2.16 A cyclist riding at 20 mph sees a stop sign and actually comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph. Which is his motion diagram? B.

27 QuickCheck 2.17 These four motion diagrams show the motion of a particle along the x-axis. 1.Which motion diagrams correspond to a positive acceleration? 2.Which motion diagrams correspond to a negative acceleration?

28 QuickCheck 2.17 These four motion diagrams show the motion of a particle along the x-axis. 1.Which motion diagrams correspond to a positive acceleration? 2.Which motion diagrams correspond to a negative acceleration? Positive Negative Positive Negative

29 QuickCheck 2.18 Mike jumps out of a tree and lands on a trampoline. The trampoline sags 2 feet before launching Mike back into the air. At the very bottom, where the sag is the greatest, Mike s acceleration is Upward. Downward. Zero.

30 QuickCheck 2.18 Mike jumps out of a tree and lands on a trampoline. The trampoline sags 2 feet before launching Mike back into the air. At the very bottom, where the sag is the greatest, Mike s acceleration is Upward. Downward. Zero.

31 QuickCheck 2.19 A cart slows down while moving away from the origin. What do the position and velocity graphs look like?

32 QuickCheck 2.19 A cart slows down while moving away from the origin. What do the position and velocity graphs look like? D.

33 QuickCheck 2.20 A cart speeds up toward the origin. What do the position and velocity graphs look like?

34 QuickCheck 2.20 A cart speeds up toward the origin. What do the position and velocity graphs look like? C.

35 QuickCheck 2.21 A cart speeds up while moving away from the origin. What do the velocity and acceleration graphs look like?

36 QuickCheck 2.21 A cart speeds up while moving away from the origin. What do the velocity and acceleration graphs look like? B.

37 QuickCheck 2.22 Here is a motion diagram of a car speeding up on a straight road: The sign of the acceleration a x is Positive. Negative. Zero.

38 QuickCheck 2.22 Here is a motion diagram of a car speeding up on a straight road: The sign of the acceleration a x is Positive. Negative. Zero. Speeding up means v x and a x have the same sign.

39 QuickCheck 2.23 A cart slows down while moving away from the origin. What do the velocity and acceleration graphs look like?

40 QuickCheck 2.23 A cart slows down while moving away from the origin. What do the velocity and acceleration graphs look like? C.

41 QuickCheck 2.24 A cart speeds up while moving toward the origin. What do the velocity and acceleration graphs look like?

42 QuickCheck 2.24 A cart speeds up while moving toward the origin. What do the velocity and acceleration graphs look like? C.

43 QuickCheck 2.25 Which velocity-versus-time graph goes with this acceleration graph?

44 QuickCheck 2.25 Which velocity-versus-time graph goes with this acceleration graph? E.

45 Section 2.5 Motion with Constant Acceleration

46 Motion with Constant Acceleration We can use the slope of the graph in the velocity graph to determine the acceleration of the rocket.

47 Constant Acceleration Equations We can use the acceleration to find (v x ) f at a later time t f. We have expressed this equation for motion along the x-axis, but it is a general result that will apply to any axis.

48 Constant Acceleration Equations The velocity-versus-time graph for constantacceleration motion is a straight line with value (v x ) i at time t i and slope a x. The displacement Δx during a time interval Δt is the area under the velocity-versustime graph shown in the shaded area of the figure.

49 Constant Acceleration Equations The shaded area can be subdivided into a rectangle and a triangle. Adding these areas gives

50 Constant Acceleration Equations Combining Equation 2.11 with Equation 2.12 gives us a relationship between displacement and velocity: Δx in Equation 2.13 is the displacement (not the distance!).

51 Constant Acceleration Equations For motion with constant acceleration: Velocity changes steadily: The position changes as the square of the time interval: We can also express the change in velocity in terms of distance, not time: Text: p. 43

52 Example 2.8 Coming to a stop As you drive in your car at 15 m/s (just a bit under 35 mph), you see a child s ball roll into the street ahead of you. You hit the brakes and stop as quickly as you can. In this case, you come to rest in 1.5 s. How far does your car travel as you brake to a stop? PREPARE The problem statement gives us a description of motion in words. To help us visualize the situation, FIGURE 2.30 illustrates the key features of the motion with a motion diagram and a velocity graph. The graph is based on the car slowing from 15 m/s to 0 m/s in 1.5 s.

53 Example 2.8 Coming to a stop (cont.) SOLVE We ve assumed that your car is moving to the right, so its initial velocity is (v x ) i = +15 m/s. After you come to rest, your final velocity is (v x ) f = 0 m/s. We use the definition of acceleration from Synthesis 2.1: An acceleration of -10 m/s 2 (really -10 m/s per second) means the car slows by 10 m/s every second. Now that we know the acceleration, we can compute the distance that the car moves as it comes to rest using the second constant acceleration equation in Synthesis 2.1:

54 Example 2.8 Coming to a stop (cont.) ASSESS 11 m is a little over 35 feet. That s a reasonable distance for a quick stop while traveling at about 35 mph. The purpose of the Assess step is not to prove that your solution is correct but to use common sense to recognize answers that are clearly wrong. Had you made a calculation error and ended up with an answer of 1.1 m less than 4 feet a moment s reflection should indicate that this couldn t possibly be correct.

55 Example Problem: Reaching New Heights Spud Webb, height 5'7'', was one of the shortest basketball players to play in the NBA. But he had in impressive vertical leap; he was reputedly able to jump 110 cm off the ground. To jump this high, with what speed would he leave the ground?

56 Section 2.6 Solving One- Dimensional Motion Problems

57 Problem-Solving Strategy Text: p. 45

58 Problem-Solving Strategy (cont.) Text: p. 45

59 Problem-Solving Strategy (cont.) Text: p. 45

60 Problem-Solving Strategy (cont.) Text: p. 45

61 The Pictorial Representation Text: p. 46

62 Example 2.11 Kinematics of a rocket launch A Saturn V rocket is launched straight up with a constant acceleration of 18 m/s 2. After 150 s, how fast is the rocket moving and how far has it traveled? PREPARE FIGURE 2.32 shows a visual overview of the rocket launch that includes a motion diagram, a pictorial representation, and a list of values. The visual overview shows the whole problem in a nutshell. The motion diagram illustrates the motion of the rocket. The pictorial representation (produced according to Tactics Box 2.2) shows axes, identifies the important points of the motion, and defines variables. Finally, we have included a list of values that gives the known and unknown quantities. In the visual overview we have taken the statement of the problem in words and made it much more precise. The overview contains everything you need to know about the problem.

63 Example 2.11 Kinematics of a rocket launch (cont.) SOLVE Our first task is to find the final velocity. Our list of values includes the initial velocity, the acceleration, and the time interval, so we can use the first kinematic equation of Synthesis 2.1 to find the final velocity:

64 Example 2.11 Kinematics of a rocket launch (cont.) SOLVE The distance traveled is found using the second equation in Synthesis 2.1:

65 Example 2.12 Calculating the minimum length of a runway A fully loaded Boeing 747 with all engines at full thrust accelerates at 2.6 m/s 2. Its minimum takeoff speed is 70 m/s. How much time will the plane take to reach its takeoff speed? What minimum length of runway does the plane require for takeoff? PREPARE The visual overview of FIGURE 2.33 summarizes the important details of the problem. We set x i and t i equal to zero at the starting point of the motion, when the plane is at rest and the acceleration begins. The final point of the motion is when the plane achieves the necessary takeoff speed of 70 m/s. The plane is accelerating to the right, so we will compute the time for the plane to reach a velocity of 70 m/s and the position of the plane at this time, giving us the minimum length of the runway.

66 Example 2.12 Calculating the minimum length of a runway (cont.) SOLVE First we solve for the time required for the plane to reach takeoff speed. We can use the first equation in Synthesis 2.1 to compute this time: We keep an extra significant figure here because we will use this result in the next step of the calculation.

67 Example 2.12 Calculating the minimum length of a runway (cont.) SOLVE Given the time that the plane takes to reach takeoff speed, we can compute the position of the plane when it reaches this speed using the second equation in Synthesis 2.1: Our final answers are thus that the plane will take 27 s to reach takeoff speed, with a minimum runway length of 940 m.

68 Example 2.12 Calculating the minimum length of a runway (cont.) ASSESS Think about the last time you flew; 27 s seems like a reasonable time for a plane to accelerate on takeoff. Actual runway lengths at major airports are 3000 m or more, a few times greater than the minimum length, because they have to allow for emergency stops during an aborted takeoff. (If we had calculated a distance far greater than 3000 m, we would know we had done something wrong!)

69 Example Problem: Champion Jumper The African antelope known as a springbok will occasionally jump straight up into the air, a movement known as a pronk. The speed when leaving the ground can be as high as 7.0 m/s. If a springbok leaves the ground at 7.0 m/s: How much time will it take to reach its highest point? How long will it stay in the air? When it returns to earth, how fast will it be moving?

70 Section 3.1 Using Vectors

71 Using Vectors A vector is a quantity with both a size (magnitude) and a direction. Figure 3.1 shows how to represent a particle s velocity as a vector. The particle s speed at this point is 5 m/s and it is moving in the direction indicated by the arrow.

72 Using Vectors The magnitude of a vector is represented by the letter without an arrow. In this case, the particle s speed the magnitude of the velocity vector is v = 5 m/s. The magnitude of a vector, a scalar quantity, cannot be a negative number.

73 Using Vectors The displacement vector is a straight-line connection from the initial position to the final position, regardless of the actual path. Two vectors are equal if they have the same magnitude and direction. This is regardless of the individual starting points of the vectors.

74 Vector Addition The figure shows the tip-to-tail rule of vector addition and the parallelogram rule of vector addition.

75 Multiplication by a Scalar Multiplying a vector by a positive scalar gives another vector of different magnitude but pointing in the same direction. If we multiply a vector by zero the product is a vector having zero length. The vector is known as the zero vector.

76 Multiplication by a Scalar A vector cannot have a negative magnitude. If we multiply a vector by a negative number we reverse its direction. Multiplying a vector by 1 reverses its direction without changing its length (magnitude).

77 Vector Subtraction Text: p. 67

78 Section 3.3 Coordinate Systems and Vector Components

79 Coordinate Systems A coordinate system is an artificially imposed grid that you place on a problem in order to make quantitative measurements. We will generally use Cartesian coordinates. Coordinate axes have a positive end and a negative end, separated by a zero at the origin where the two axes cross.

80 Component Vectors For a vector A and an xy-coordinate system we can define two new vectors parallel to the axes that we call the component vectors of. You can see, using the parallelogram rule, that is the vector sum of the two component vectors:

81 In class!! PHYS101